WASHINGTON (CNN) --After President Bush said he would support a constitutional amendment that would ban same-sex marriage, opponents were saying on Wednesday that the move will cost him dearly with voters, while supporters said the decision helps fire up his conservative base.

"I think it will actually encourage his base to know for sure that our president stands for the definition of marriage as a union between a man and a woman," Rep. Marilyn Musgrave, R-Colorado, told CNN's "American Morning."

Musgrave has submitted an amendment to ban same-sex marriage, but it is not clear if it, or any similar amendment, will be able to win the necessary two-thirds majority in both houses of Congress for it to be sent to states for ratification.

Railing against Gavin Newsom, whom she called "a rogue mayor in San Francisco," for ordering the issuance of marriage licenses to same-sex couples, Musgrave called Bush's action "an encouragement to people who believe in the traditional definition of marriage." (California high court may get same-sex marriage)

"I don't think he's going to lose votes. I think he's going to gain votes. I think the conservatives sometimes get disillusioned and decide to stay home, and feel like it doesn't really make any difference. But I think they are going to be encouraged to come out and vote," she said.

But more moderate Republicans and independents may respond very differently, leaders of two gay political organizations told CNN.

Patrick Guerriero, executive director of the Log Cabin Republicans, told "American Morning," "This is a dramatically bad step for the president. He might get a little bump in the polls for a few days, but we all remember in 1992 when Pat Buchanan declared a cultural war on the country and it led to the defeat of the first President Bush. This is not a way to win an election -- it's a way to divide the American family."

He added, "We can't sugarcoat this. This amendment was written by the radical right in an attempt to make sure gay and lesbian families who want tax fairness won't get it." (More reaction)

Numerous polls show that while the majority of Americans oppose gay marriage, they are split over whether to support an amendment.

Candace Gingrich, with the Human Rights Campaign, the largest gay and lesbian political organization, said Wednesday that Bush is trying to draw attention away from focus on "the falling poll numbers, on the deficit and the lack of jobs that have been produced."

"In addition to those one million gay Republicansreported to have voted for Bush, we are talking about their friends and family members who care about this issue. And also that 1 million people is an important number when you consider that President Bush lost the popular vote in 2000."

Bush received about 543,000 fewer votes in the 2000 presidential election than Democrat Al Gore.

Bush's announcement Tuesday, which the White House said followed a good deal of serious reflection, contradicts Bush's own statement four years ago that states should be left to "do what they want to do" regarding same-sex marriage.

Asked repeatedly what had changed Bush's mind, White House spokesman Scott McClellan said only, "His views have always been well known on this very issue."

It was during a CNN Republican primary debate that year in South Carolina that he was asked about gay marriage. Bush said he would "stand up and say I don't support gay marriage."

CNN's Larry King asked, "If a state were voting on gay marriage, you would suggest to that state not to approve it?"

"The state can do what they want to do," Bush responded.

Although he took no questions Tuesday, and the White House did not explain the statement from 2000, Bush emphasized in his announcement that moves by several justices in Massachusetts, Newsom in San Francisco, and officials in a county in New Mexico "created confusion on an issue that requires clarity."

"The union of a man and a woman is the most enduring human institution, honored and encouraged in all cultures and by every religious faith," he said, adding that the nation must "prevent the meaning of marriage from being changed forever." (Transcript of Bush comments)

Bush also said an amendment should leave "state legislatures free to make their own choices in defining arrangements other than marriage" -- language that could leave the door open to civil unions, which could allow same-sex couples some or all of the legal rights of marriage.

As governor of Texas, Bush opposed civil unions for same-sex couples.

Amending the U.S. Constitution is difficult, requiring a two-thirds majority each in the House and Senate and ratification by three-fourths, or 38, of the 50 states. Besides the Bill of Rights, the Constitution has been amended only 17 times in 215 years, most recently in 1992. (Challenges in passing an amendment)

John Feehery, a spokesman for Speaker Dennis Hastert of Illinois, said House Republican leaders would be hard-pressed to round up the 291 votes needed to pass an amendment.

Amy Call, a spokeswoman for Senate Majority Leader Bill Frist of Tennessee, said the Senate Judiciary Committee will hold a hearing on the measure next week. Asked if it has the 67 votes needed to pass the Senate, she said, "It'll be close."

Cheney comments

Vice President Dick Cheney's stance has also been called into question.

He recently has said he would support Bush's decision on the matter.

But at a vice presidential debate in 2000, Cheney was asked, "Should a male who loves a male and a female who loves a female have all the constitutional rights enjoyed by every American citizen?"

Cheney responded, "People should be free to enter into any kind of relationship they want to enter into. It's really no one else's business, in terms of trying to regulate or prohibit behavior in that regard."

He added, "I think different states are likely to come to different conclusions, and that's appropriate. I don't think there should necessarily be a federal policy in this area. I try to be open-minded about it as much as I can and tolerant of those relationships. ... (I) wrestle with the extent of which there ought to be legal sanction of those relationships. I think we ought to do everything we can to tolerate and accommodate whatever kind of relationships people want to enter into."

Cheney's office says that like Bush, the vice president is concerned that the 1996 Defense of Marriage Act -- which defined marriage as the union of a man and a woman -- is under attack because of actions by officials in certain states.

Cheney, whose daughter is a lesbian and well-known figure in the Colorado gay community, was quoted in two Colorado newspapers as saying that he would support Bush's decision on an amendment no matter what it was.